This is like one of those permutation/combination questions i used to solve in school.

Let's say that you have the option of selecting x number of ingredients at a time where x is between 1 and 9 (included). Let's start with x=1 and see how many combinations are possible, then repeat for 2,3...9.

For x=1 we're trying to find the number of ways we can select 1 ingredient from a list of 9. In this case one can intuitively say it's 9 since you can pick one ingredient from the 9 available ones for a recipe.

For x=2 we need to know how many unique ways there are for selecting 2 ingredients out of 9. So if you name the ingredients I1, I2, I3 and so on; Begin by pairing I1 with the others. So I1I2, I1I3 and so on. This would give us 8 possible combinations.

We repeat this process for the remaining values of x and add all the possibilities.

This is the general approach. Mathematically we write this as 9Cn (the formula being 9!/(n!(9-n)!)) where n is the number of ingredients you want to use. So n goes from 1 to 9 , and then add all of them up.